ROBUST STABILIZATION OF LINEAR-SYSTEMS IN THE PRESENCE OF GAUSSIAN PERTURBATION OF PARAMETERS

Stabilization of linear systems in state space in the presence of para metric perturbations is considered. The perturbed system is represente d by a matrix differential equation with the elements of the matrices given by Gaussian processes with known mean and covariance. Using meth ods from stochastic control theory, certain pole-placement-like result s are derived which hold in the mean square sense. In the absence of a ny perturbation, these results reduce to the well-known results of pol e placement for deterministic linear systems, Minimizing the real part of the largest eigenvalue of the expected closed-loop matrix, we obta in the optimal feedback gain that stabilizes the system at the fastest possible rate. The question of existence of a guaranteed stabilizing feedback is also investigated. As a consequence of the main result we obtain a method of designing fault-tolerant systems that will survive in the events of catastrophic controller failure. An extension of the Luenberger observer for uncertain systems is also presented. (C) 1998 John Wiley & Sons, Ltd.